MATLAB: Solve a second order differential equation

ode

Hi, I am completely new to Matlab and am looking to solve a simple second order differential equation:
y''+w^2*y=0 IC: y(0)=0, y'(0)=1 BC=[0,pi]
I am looking to solve for both y(x) and y'(x)
I understand this is a simple equation to solve and have done it fine on paper. However I have been trying different ways to solve it on matlab but to no avail. I have tried both dsolve and ode45 functions but did not quite understand what I was doing. Any help would be great. Thanks in advance, Ben

Best Answer

% x1=y
%x2=dy
Then
%dx1=dy=x2
%dx2=d2y=-w^2*y=-w^2*x1
save this function as yourfcn
function dx=yourfcn(t,x)
w=1
dx(1)=x(2)
dx(2)=-w^2*x(1)
Then call the ode45 function
[t,x]=ode45(@yourfcn,[0,pi],[0 0])
Then deduce y
y=x(:,1)
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